/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x1) (RULES 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ) Problem 1: Dependency Pairs Processor: -> Pairs: 0#(0(0(0(4(5(x1)))))) -> 0#(2(3(2(4(1(5(2(3(5(x1)))))))))) 0#(0(0(0(4(5(x1)))))) -> 1#(5(2(3(5(x1))))) 0#(0(0(0(4(5(x1)))))) -> 3#(5(x1)) 0#(0(0(0(4(5(x1)))))) -> 3#(2(4(1(5(2(3(5(x1)))))))) 0#(0(0(0(4(5(x1)))))) -> 4#(1(5(2(3(5(x1)))))) 0#(0(0(0(4(5(x1)))))) -> 5#(2(3(5(x1)))) 0#(0(0(4(0(x1))))) -> 0#(3(4(x1))) 0#(0(0(4(0(x1))))) -> 1#(2(2(0(3(4(x1)))))) 0#(0(0(4(0(x1))))) -> 3#(4(4(4(1(2(2(0(3(4(x1)))))))))) 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(1(2(2(0(3(4(x1))))))) 0#(0(0(4(0(x1))))) -> 4#(4(1(2(2(0(3(4(x1)))))))) 0#(0(0(4(0(x1))))) -> 4#(4(4(1(2(2(0(3(4(x1))))))))) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 3#(2(2(1(2(4(1(1(0(4(x1)))))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(3(2(1(4(3(5(5(x1)))))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(2(1(3(2(1(4(3(5(5(x1)))))))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(2(1(4(3(5(5(x1))))))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(2(2(3(5(2(2(1(1(4(x1)))))))))) 0#(0(4(5(3(0(x1)))))) -> 3#(5(2(2(1(1(4(x1))))))) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(4(5(3(0(x1)))))) -> 5#(2(2(1(1(4(x1)))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(2(3(2(2(0(0(3(1(3(x1)))))))))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(2(2(0(0(3(1(3(x1)))))))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(0(5(2(5(2(1(x1))))))) -> 3#(4(2(2(1(2(0(x1))))))) 0#(0(5(2(5(2(1(x1))))))) -> 3#(5(3(4(2(2(1(2(0(x1))))))))) 0#(0(5(2(5(2(1(x1))))))) -> 4#(2(2(1(2(0(x1)))))) 0#(0(5(2(5(2(1(x1))))))) -> 5#(3(4(2(2(1(2(0(x1)))))))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(2(2(4(3(3(3(0(2(0(x1)))))))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 3#(3(2(2(3(2(4(2(4(x1))))))))) 0#(1(0(x1))) -> 3#(2(4(2(4(x1))))) 0#(1(0(x1))) -> 3#(2(2(3(2(4(2(4(x1)))))))) 0#(1(0(x1))) -> 4#(2(4(x1))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(3(2(1(2(5(5(3(x1)))))))) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(2(1(3(2(1(2(5(5(3(x1)))))))))) 0#(1(5(3(1(1(x1)))))) -> 3#(2(1(2(5(5(3(x1))))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(3(0(0(0(0(0(x1))))))) -> 5#(2(3(1(0(2(4(4(x1)))))))) 0#(4(0(0(0(4(3(x1))))))) -> 0#(5(5(2(1(3(2(3(3(3(x1)))))))))) 0#(4(0(0(0(4(3(x1))))))) -> 1#(3(2(3(3(3(x1)))))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(0(0(0(4(3(x1))))))) -> 3#(2(3(3(3(x1))))) 0#(4(0(0(0(4(3(x1))))))) -> 5#(5(2(1(3(2(3(3(3(x1))))))))) 0#(4(0(0(0(4(3(x1))))))) -> 5#(2(1(3(2(3(3(3(x1)))))))) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 3#(2(0(5(4(3(1(2(1(x1))))))))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 3#(2(1(0(5(2(0(3(3(4(x1)))))))))) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(1(1(5(0(0(x1))))))) -> 5#(2(0(3(3(4(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(2(1(3(4(4(1(0(1(x1))))))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(3(3(4(2(3(2(1(x1)))))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(4(1(2(x1))))) -> 3#(3(4(2(3(2(1(x1))))))) 0#(5(4(1(2(x1))))) -> 3#(4(2(3(2(1(x1)))))) 0#(5(4(1(2(x1))))) -> 3#(2(1(3(3(4(2(3(2(1(x1)))))))))) 0#(5(4(1(2(x1))))) -> 3#(2(1(x1))) 0#(5(4(1(2(x1))))) -> 4#(2(3(2(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 1#(2(3(2(3(0(4(x1))))))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(1(2(3(2(3(0(4(x1)))))))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(3(1(2(3(2(3(0(4(x1))))))))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(2(3(0(4(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 1#(2(3(2(3(3(x1)))))) 0#(2(0(0(1(1(x1)))))) -> 3#(1(2(3(2(3(3(x1))))))) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(4(2(3(1(2(3(2(3(3(x1)))))))))) 0#(2(0(0(1(1(x1)))))) -> 3#(2(3(3(x1)))) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(0(1(1(x1)))))) -> 4#(2(3(1(2(3(2(3(3(x1))))))))) 0#(2(0(3(0(0(2(x1))))))) -> 1#(3(4(4(5(2(3(x1))))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(1(3(4(4(5(2(3(x1)))))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(4(4(5(2(3(x1)))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(2(3(1(3(4(4(5(2(3(x1)))))))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 4#(4(5(2(3(x1))))) 0#(2(0(3(0(0(2(x1))))))) -> 4#(5(2(3(x1)))) 0#(2(0(3(0(0(2(x1))))))) -> 5#(2(3(x1))) 0#(2(4(0(1(5(4(x1))))))) -> 0#(1(3(2(1(5(3(4(x1)))))))) 0#(2(4(0(1(5(4(x1))))))) -> 1#(3(2(1(5(3(4(x1))))))) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 3#(2(0(1(3(2(1(5(3(4(x1)))))))))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(2(1(5(3(4(x1)))))) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 0#(4(1(1(2(2(3(2(5(3(x1)))))))))) 0#(2(2(5(0(4(3(x1))))))) -> 1#(1(2(2(3(2(5(3(x1)))))))) 0#(2(2(5(0(4(3(x1))))))) -> 1#(2(2(3(2(5(3(x1))))))) 0#(2(2(5(0(4(3(x1))))))) -> 3#(2(5(3(x1)))) 0#(2(2(5(0(4(3(x1))))))) -> 4#(1(1(2(2(3(2(5(3(x1))))))))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 1#(1(2(3(2(3(2(4(3(0(x1)))))))))) 1#(0(0(3(0(x1))))) -> 1#(2(3(2(3(2(4(3(0(x1))))))))) 1#(0(0(3(0(x1))))) -> 3#(2(3(2(4(3(0(x1))))))) 1#(0(0(3(0(x1))))) -> 3#(2(4(3(0(x1))))) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 3#(2(4(4(4(x1))))) 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1#(4(1(3(0(4(3(x1))))))) -> 5#(1(2(3(2(2(5(1(x1)))))))) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(1(3(2(1(x1))))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(3(2(1(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(5(4(3(2(1(1(3(2(1(x1)))))))))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(5(0(0(5(3(3(x1))))))) -> 3#(2(1(1(3(2(1(x1))))))) 1#(5(0(0(5(3(3(x1))))))) -> 3#(2(1(x1))) 1#(5(0(0(5(3(3(x1))))))) -> 4#(3(2(1(1(3(2(1(x1)))))))) 1#(5(0(0(5(3(3(x1))))))) -> 5#(4(3(2(1(1(3(2(1(x1))))))))) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 1#(3(3(2(2(3(5(1(0(3(x1)))))))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(3(2(2(3(5(1(0(3(x1))))))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(2(2(3(5(1(0(3(x1)))))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(3(3(2(0(5(3(1(5(x1))))))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 3#(3(2(0(5(3(1(5(x1)))))))) 3#(0(0(1(3(5(x1)))))) -> 3#(2(0(5(3(1(5(x1))))))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 3#(1(4(0(1(2(x1)))))) -> 3#(2(2(1(0(3(1(1(2(x1))))))))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(0(4(1(4(x1))))))) -> 3#(2(1(1(2(1(0(0(x1)))))))) 4#(0(0(0(4(1(4(x1))))))) -> 4#(3(2(1(1(2(1(0(0(x1))))))))) 4#(0(0(0(4(1(4(x1))))))) -> 4#(4(3(2(1(1(2(1(0(0(x1)))))))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 3#(2(2(1(2(0(5(4(4(1(x1)))))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 0#(3(2(3(3(5(4(1(5(x1))))))))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(0(3(2(3(3(5(4(1(5(x1)))))))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(2(3(3(5(4(1(5(x1)))))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(3(5(2(2(2(3(4(4(0(x1)))))))))) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 3#(5(2(2(2(3(4(4(0(x1))))))))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(0(4(5(2(4(x1))))))) -> 5#(2(2(2(3(4(4(0(x1)))))))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(3(2(3(4(3(1(0(3(x1))))))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(2(3(4(3(1(0(3(x1)))))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(3(2(3(4(3(1(0(3(x1)))))))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 1#(2(2(0(0(2(1(1(4(x1))))))))) 4#(0(4(1(4(0(0(x1))))))) -> 3#(1(2(2(0(0(2(1(1(4(x1)))))))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 1#(3(2(4(3(4(x1)))))) 4#(1(0(5(4(1(4(x1))))))) -> 1#(2(1(3(2(4(3(4(x1)))))))) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 3#(2(4(3(4(x1))))) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(0(5(4(1(4(x1))))))) -> 5#(1(2(1(3(2(4(3(4(x1))))))))) 4#(1(4(0(3(1(0(x1))))))) -> 0#(2(2(2(5(1(4(x1))))))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 3#(2(0(2(2(2(5(1(4(x1))))))))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 5#(3(2(0(2(2(2(5(1(4(x1)))))))))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(3(2(0(4(x1))))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 1#(3(0(3(2(0(4(x1))))))) 4#(1(2(5(4(0(0(x1))))))) -> 3#(0(3(2(0(4(x1)))))) 4#(1(2(5(4(0(0(x1))))))) -> 3#(2(0(4(x1)))) 4#(1(2(5(4(0(0(x1))))))) -> 4#(5(1(3(0(3(2(0(4(x1))))))))) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(1(2(5(4(0(0(x1))))))) -> 5#(1(3(0(3(2(0(4(x1)))))))) 4#(3(5(5(4(1(0(x1))))))) -> 1#(3(4(5(2(3(3(4(x1)))))))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(5(2(3(3(4(x1))))))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 3#(5(1(3(4(5(2(3(3(4(x1)))))))))) 4#(3(5(5(4(1(0(x1))))))) -> 4#(5(2(3(3(4(x1)))))) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 5#(1(3(4(5(2(3(3(4(x1))))))))) 4#(3(5(5(4(1(0(x1))))))) -> 5#(2(3(3(4(x1))))) 4#(5(0(2(4(1(x1)))))) -> 1#(4(2(3(2(2(3(4(1(x1))))))))) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 4#(5(0(2(4(1(x1)))))) -> 3#(2(2(3(4(1(x1)))))) 4#(5(0(2(4(1(x1)))))) -> 4#(2(3(2(2(3(4(1(x1)))))))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(2(2(3(0(5(4(x1))))))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(3(2(2(3(0(5(4(x1)))))))) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(0(0(1(4(0(x1))))))) -> 5#(2(5(3(2(2(3(0(5(4(x1)))))))))) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 3#(2(0(2(x1)))) 5#(0(5(0(1(5(2(x1))))))) -> 3#(2(3(2(4(3(2(0(2(x1))))))))) 5#(0(5(0(1(5(2(x1))))))) -> 3#(2(4(3(2(0(2(x1))))))) 5#(0(5(0(1(5(2(x1))))))) -> 4#(3(2(0(2(x1))))) 5#(0(5(0(1(5(2(x1))))))) -> 5#(3(2(3(2(4(3(2(0(2(x1)))))))))) 5#(0(2(5(4(4(0(x1))))))) -> 0#(3(2(2(1(1(3(4(x1)))))))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(2(2(1(1(3(4(x1))))))) 5#(0(2(5(4(4(0(x1))))))) -> 4#(0(3(2(2(1(1(3(4(x1))))))))) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(0(2(5(4(4(0(x1))))))) -> 5#(4(0(3(2(2(1(1(3(4(x1)))))))))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(0(1(4(3(1(x1))))))) -> 3#(2(2(1(2(1(0(0(3(1(x1)))))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(2(2(1(5(5(3(5(1(x1))))))))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(2(2(1(5(5(3(5(1(x1)))))))))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 3#(2(4(3(x1)))) 5#(4(0(4(1(0(3(x1))))))) -> 3#(2(2(4(4(3(2(4(3(x1))))))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(2(4(3(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) 5#(4(0(4(1(0(3(x1))))))) -> 4#(4(3(2(4(3(x1)))))) 5#(4(0(4(1(0(3(x1))))))) -> 5#(3(2(2(4(4(3(2(4(3(x1)))))))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: SCC Processor: -> Pairs: 0#(0(0(0(4(5(x1)))))) -> 0#(2(3(2(4(1(5(2(3(5(x1)))))))))) 0#(0(0(0(4(5(x1)))))) -> 1#(5(2(3(5(x1))))) 0#(0(0(0(4(5(x1)))))) -> 3#(5(x1)) 0#(0(0(0(4(5(x1)))))) -> 3#(2(4(1(5(2(3(5(x1)))))))) 0#(0(0(0(4(5(x1)))))) -> 4#(1(5(2(3(5(x1)))))) 0#(0(0(0(4(5(x1)))))) -> 5#(2(3(5(x1)))) 0#(0(0(4(0(x1))))) -> 0#(3(4(x1))) 0#(0(0(4(0(x1))))) -> 1#(2(2(0(3(4(x1)))))) 0#(0(0(4(0(x1))))) -> 3#(4(4(4(1(2(2(0(3(4(x1)))))))))) 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(1(2(2(0(3(4(x1))))))) 0#(0(0(4(0(x1))))) -> 4#(4(1(2(2(0(3(4(x1)))))))) 0#(0(0(4(0(x1))))) -> 4#(4(4(1(2(2(0(3(4(x1))))))))) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 3#(2(2(1(2(4(1(1(0(4(x1)))))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(3(2(1(4(3(5(5(x1)))))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(2(1(3(2(1(4(3(5(5(x1)))))))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(2(1(4(3(5(5(x1))))))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(2(2(3(5(2(2(1(1(4(x1)))))))))) 0#(0(4(5(3(0(x1)))))) -> 3#(5(2(2(1(1(4(x1))))))) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(4(5(3(0(x1)))))) -> 5#(2(2(1(1(4(x1)))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(2(3(2(2(0(0(3(1(3(x1)))))))))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(2(2(0(0(3(1(3(x1)))))))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(0(5(2(5(2(1(x1))))))) -> 3#(4(2(2(1(2(0(x1))))))) 0#(0(5(2(5(2(1(x1))))))) -> 3#(5(3(4(2(2(1(2(0(x1))))))))) 0#(0(5(2(5(2(1(x1))))))) -> 4#(2(2(1(2(0(x1)))))) 0#(0(5(2(5(2(1(x1))))))) -> 5#(3(4(2(2(1(2(0(x1)))))))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(2(2(4(3(3(3(0(2(0(x1)))))))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 3#(3(2(2(3(2(4(2(4(x1))))))))) 0#(1(0(x1))) -> 3#(2(4(2(4(x1))))) 0#(1(0(x1))) -> 3#(2(2(3(2(4(2(4(x1)))))))) 0#(1(0(x1))) -> 4#(2(4(x1))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(3(2(1(2(5(5(3(x1)))))))) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(2(1(3(2(1(2(5(5(3(x1)))))))))) 0#(1(5(3(1(1(x1)))))) -> 3#(2(1(2(5(5(3(x1))))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(3(0(0(0(0(0(x1))))))) -> 5#(2(3(1(0(2(4(4(x1)))))))) 0#(4(0(0(0(4(3(x1))))))) -> 0#(5(5(2(1(3(2(3(3(3(x1)))))))))) 0#(4(0(0(0(4(3(x1))))))) -> 1#(3(2(3(3(3(x1)))))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(0(0(0(4(3(x1))))))) -> 3#(2(3(3(3(x1))))) 0#(4(0(0(0(4(3(x1))))))) -> 5#(5(2(1(3(2(3(3(3(x1))))))))) 0#(4(0(0(0(4(3(x1))))))) -> 5#(2(1(3(2(3(3(3(x1)))))))) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 3#(2(0(5(4(3(1(2(1(x1))))))))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 3#(2(1(0(5(2(0(3(3(4(x1)))))))))) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(1(1(5(0(0(x1))))))) -> 5#(2(0(3(3(4(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(2(1(3(4(4(1(0(1(x1))))))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(3(3(4(2(3(2(1(x1)))))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(4(1(2(x1))))) -> 3#(3(4(2(3(2(1(x1))))))) 0#(5(4(1(2(x1))))) -> 3#(4(2(3(2(1(x1)))))) 0#(5(4(1(2(x1))))) -> 3#(2(1(3(3(4(2(3(2(1(x1)))))))))) 0#(5(4(1(2(x1))))) -> 3#(2(1(x1))) 0#(5(4(1(2(x1))))) -> 4#(2(3(2(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 1#(2(3(2(3(0(4(x1))))))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(1(2(3(2(3(0(4(x1)))))))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(3(1(2(3(2(3(0(4(x1))))))))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(2(3(0(4(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 1#(2(3(2(3(3(x1)))))) 0#(2(0(0(1(1(x1)))))) -> 3#(1(2(3(2(3(3(x1))))))) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(4(2(3(1(2(3(2(3(3(x1)))))))))) 0#(2(0(0(1(1(x1)))))) -> 3#(2(3(3(x1)))) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(0(1(1(x1)))))) -> 4#(2(3(1(2(3(2(3(3(x1))))))))) 0#(2(0(3(0(0(2(x1))))))) -> 1#(3(4(4(5(2(3(x1))))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(1(3(4(4(5(2(3(x1)))))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(4(4(5(2(3(x1)))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(2(3(1(3(4(4(5(2(3(x1)))))))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 4#(4(5(2(3(x1))))) 0#(2(0(3(0(0(2(x1))))))) -> 4#(5(2(3(x1)))) 0#(2(0(3(0(0(2(x1))))))) -> 5#(2(3(x1))) 0#(2(4(0(1(5(4(x1))))))) -> 0#(1(3(2(1(5(3(4(x1)))))))) 0#(2(4(0(1(5(4(x1))))))) -> 1#(3(2(1(5(3(4(x1))))))) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 3#(2(0(1(3(2(1(5(3(4(x1)))))))))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(2(1(5(3(4(x1)))))) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 0#(4(1(1(2(2(3(2(5(3(x1)))))))))) 0#(2(2(5(0(4(3(x1))))))) -> 1#(1(2(2(3(2(5(3(x1)))))))) 0#(2(2(5(0(4(3(x1))))))) -> 1#(2(2(3(2(5(3(x1))))))) 0#(2(2(5(0(4(3(x1))))))) -> 3#(2(5(3(x1)))) 0#(2(2(5(0(4(3(x1))))))) -> 4#(1(1(2(2(3(2(5(3(x1))))))))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 1#(1(2(3(2(3(2(4(3(0(x1)))))))))) 1#(0(0(3(0(x1))))) -> 1#(2(3(2(3(2(4(3(0(x1))))))))) 1#(0(0(3(0(x1))))) -> 3#(2(3(2(4(3(0(x1))))))) 1#(0(0(3(0(x1))))) -> 3#(2(4(3(0(x1))))) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 3#(2(4(4(4(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(2(2(5(3(2(4(4(4(x1))))))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(0(3(1(0(0(0(x1))))))) -> 5#(3(2(4(4(4(x1)))))) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 3#(2(2(1(2(4(5(4(3(5(x1)))))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 3#(3(2(1(4(4(x1)))))) 1#(4(0(3(0(4(x1)))))) -> 3#(2(1(4(4(x1))))) 1#(4(0(3(0(4(x1)))))) -> 3#(2(2(5(3(3(2(1(4(4(x1)))))))))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(0(3(0(4(x1)))))) -> 5#(3(3(2(1(4(4(x1))))))) 1#(4(1(3(0(4(3(x1))))))) -> 1#(3(5(1(2(3(2(2(5(1(x1)))))))))) 1#(4(1(3(0(4(3(x1))))))) -> 1#(2(3(2(2(5(1(x1))))))) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 3#(5(1(2(3(2(2(5(1(x1))))))))) 1#(4(1(3(0(4(3(x1))))))) -> 3#(2(2(5(1(x1))))) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(2(3(2(2(5(1(x1)))))))) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(1(3(2(1(x1))))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(3(2(1(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(5(4(3(2(1(1(3(2(1(x1)))))))))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(5(0(0(5(3(3(x1))))))) -> 3#(2(1(1(3(2(1(x1))))))) 1#(5(0(0(5(3(3(x1))))))) -> 3#(2(1(x1))) 1#(5(0(0(5(3(3(x1))))))) -> 4#(3(2(1(1(3(2(1(x1)))))))) 1#(5(0(0(5(3(3(x1))))))) -> 5#(4(3(2(1(1(3(2(1(x1))))))))) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 1#(3(3(2(2(3(5(1(0(3(x1)))))))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(3(2(2(3(5(1(0(3(x1))))))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(2(2(3(5(1(0(3(x1)))))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(3(3(2(0(5(3(1(5(x1))))))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 3#(3(2(0(5(3(1(5(x1)))))))) 3#(0(0(1(3(5(x1)))))) -> 3#(2(0(5(3(1(5(x1))))))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 3#(1(4(0(1(2(x1)))))) -> 3#(2(2(1(0(3(1(1(2(x1))))))))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(0(4(1(4(x1))))))) -> 3#(2(1(1(2(1(0(0(x1)))))))) 4#(0(0(0(4(1(4(x1))))))) -> 4#(3(2(1(1(2(1(0(0(x1))))))))) 4#(0(0(0(4(1(4(x1))))))) -> 4#(4(3(2(1(1(2(1(0(0(x1)))))))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 3#(2(2(1(2(0(5(4(4(1(x1)))))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 0#(3(2(3(3(5(4(1(5(x1))))))))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(0(3(2(3(3(5(4(1(5(x1)))))))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(2(3(3(5(4(1(5(x1)))))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(3(5(2(2(2(3(4(4(0(x1)))))))))) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 3#(5(2(2(2(3(4(4(0(x1))))))))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(0(4(5(2(4(x1))))))) -> 5#(2(2(2(3(4(4(0(x1)))))))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(3(2(3(4(3(1(0(3(x1))))))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(2(3(4(3(1(0(3(x1)))))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(3(2(3(4(3(1(0(3(x1)))))))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 1#(2(2(0(0(2(1(1(4(x1))))))))) 4#(0(4(1(4(0(0(x1))))))) -> 3#(1(2(2(0(0(2(1(1(4(x1)))))))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 1#(3(2(4(3(4(x1)))))) 4#(1(0(5(4(1(4(x1))))))) -> 1#(2(1(3(2(4(3(4(x1)))))))) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 3#(2(4(3(4(x1))))) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(0(5(4(1(4(x1))))))) -> 5#(1(2(1(3(2(4(3(4(x1))))))))) 4#(1(4(0(3(1(0(x1))))))) -> 0#(2(2(2(5(1(4(x1))))))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 3#(2(0(2(2(2(5(1(4(x1))))))))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 5#(3(2(0(2(2(2(5(1(4(x1)))))))))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(3(2(0(4(x1))))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 1#(3(0(3(2(0(4(x1))))))) 4#(1(2(5(4(0(0(x1))))))) -> 3#(0(3(2(0(4(x1)))))) 4#(1(2(5(4(0(0(x1))))))) -> 3#(2(0(4(x1)))) 4#(1(2(5(4(0(0(x1))))))) -> 4#(5(1(3(0(3(2(0(4(x1))))))))) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(1(2(5(4(0(0(x1))))))) -> 5#(1(3(0(3(2(0(4(x1)))))))) 4#(3(5(5(4(1(0(x1))))))) -> 1#(3(4(5(2(3(3(4(x1)))))))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(5(2(3(3(4(x1))))))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 3#(5(1(3(4(5(2(3(3(4(x1)))))))))) 4#(3(5(5(4(1(0(x1))))))) -> 4#(5(2(3(3(4(x1)))))) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 5#(1(3(4(5(2(3(3(4(x1))))))))) 4#(3(5(5(4(1(0(x1))))))) -> 5#(2(3(3(4(x1))))) 4#(5(0(2(4(1(x1)))))) -> 1#(4(2(3(2(2(3(4(1(x1))))))))) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 4#(5(0(2(4(1(x1)))))) -> 3#(2(2(3(4(1(x1)))))) 4#(5(0(2(4(1(x1)))))) -> 4#(2(3(2(2(3(4(1(x1)))))))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(2(2(3(0(5(4(x1))))))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(3(2(2(3(0(5(4(x1)))))))) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(0(0(1(4(0(x1))))))) -> 5#(2(5(3(2(2(3(0(5(4(x1)))))))))) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 3#(2(0(2(x1)))) 5#(0(5(0(1(5(2(x1))))))) -> 3#(2(3(2(4(3(2(0(2(x1))))))))) 5#(0(5(0(1(5(2(x1))))))) -> 3#(2(4(3(2(0(2(x1))))))) 5#(0(5(0(1(5(2(x1))))))) -> 4#(3(2(0(2(x1))))) 5#(0(5(0(1(5(2(x1))))))) -> 5#(3(2(3(2(4(3(2(0(2(x1)))))))))) 5#(0(2(5(4(4(0(x1))))))) -> 0#(3(2(2(1(1(3(4(x1)))))))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(2(2(1(1(3(4(x1))))))) 5#(0(2(5(4(4(0(x1))))))) -> 4#(0(3(2(2(1(1(3(4(x1))))))))) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(0(2(5(4(4(0(x1))))))) -> 5#(4(0(3(2(2(1(1(3(4(x1)))))))))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(0(1(4(3(1(x1))))))) -> 3#(2(2(1(2(1(0(0(3(1(x1)))))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(2(2(1(5(5(3(5(1(x1))))))))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(2(2(1(5(5(3(5(1(x1)))))))))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 3#(2(4(3(x1)))) 5#(4(0(4(1(0(3(x1))))))) -> 3#(2(2(4(4(3(2(4(3(x1))))))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(2(4(3(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) 5#(4(0(4(1(0(3(x1))))))) -> 4#(4(3(2(4(3(x1)))))) 5#(4(0(4(1(0(3(x1))))))) -> 5#(3(2(2(4(4(3(2(4(3(x1)))))))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(0(0(4(5(x1)))))) -> 3#(5(x1)) 0#(0(0(4(0(x1))))) -> 0#(3(4(x1))) 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(0(0(4(5(x1)))))) -> 3#(5(x1)) 0#(0(0(4(0(x1))))) -> 0#(3(4(x1))) 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(0(0(4(0(x1))))) -> 0#(3(4(x1))) 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(0(4(0(x1))))) -> 0#(3(4(x1))) 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(0(4(0(x1))))) -> 0#(3(4(x1))) 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(0(4(0(x1))))) -> 3#(4(x1)) 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(0(4(0(x1))))) -> 4#(x1) 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(0(2(0(4(x1)))))) -> 1#(0(4(x1))) 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(0(2(0(4(x1)))))) -> 1#(1(0(4(x1)))) 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(0(2(0(4(x1)))))) -> 1#(2(4(1(1(0(4(x1))))))) 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(0(2(0(4(x1)))))) -> 4#(1(1(0(4(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 1#(4(3(5(5(x1))))) 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 3#(5(5(x1))) 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 4#(3(5(5(x1)))) 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(1(2(3(0(5(x1))))))) -> 5#(5(x1)) 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(4(5(3(0(x1)))))) -> 1#(1(4(x1))) 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(4(5(3(0(x1)))))) -> 1#(4(x1)) 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(4(5(3(0(x1)))))) -> 4#(x1) 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 0#(0(3(1(3(x1))))) 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 0#(3(1(3(x1)))) 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 1#(3(x1)) 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 3#(1(3(x1))) 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(5(4(2(0(2(x1))))))) -> 3#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(5(2(5(2(1(x1))))))) -> 0#(x1) 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(5(2(5(2(1(x1))))))) -> 1#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 0#(2(0(x1))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 3#(0(2(0(x1)))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(0(2(0(x1))))) 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 3#(3(3(0(2(0(x1)))))) 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(0(5(5(2(0(x1))))))) -> 4#(3(3(3(0(2(0(x1))))))) 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(0(x1))) -> 4#(x1) 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(5(3(1(1(x1)))))) -> 1#(2(5(5(3(x1))))) 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(5(3(1(1(x1)))))) -> 3#(x1) 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(5(3(1(1(x1)))))) -> 5#(3(x1)) 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(1(5(3(1(1(x1)))))) -> 5#(5(3(x1))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 0#(5(2(3(1(0(2(4(4(x1))))))))) 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 0#(2(4(4(x1)))) 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 1#(0(2(4(4(x1))))) 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 3#(1(0(2(4(4(x1)))))) 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 4#(4(x1)) 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(3(0(0(0(0(0(x1))))))) -> 4#(x1) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(3(x1))) 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(4(0(0(0(4(3(x1))))))) -> 3#(3(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 0#(2(4(4(x1)))) 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 1#(2(3(0(2(4(4(x1))))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 3#(0(2(4(4(x1))))) 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 3#(5(1(2(3(0(2(4(4(x1))))))))) 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 4#(4(x1)) 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(4(5(5(5(0(4(x1))))))) -> 5#(1(2(3(0(2(4(4(x1)))))))) 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 0#(5(4(3(1(2(1(x1))))))) 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 1#(2(1(x1))) 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 1#(x1) 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 3#(1(2(1(x1)))) 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 4#(3(1(2(1(x1))))) 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(0(0(0(2(x1)))))) -> 5#(4(3(1(2(1(x1)))))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 0#(3(3(4(x1)))) 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 0#(5(2(0(3(3(4(x1))))))) 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 1#(0(5(2(0(3(3(4(x1)))))))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 3#(3(4(x1))) 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 3#(4(x1)) 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(1(1(5(0(0(x1))))))) -> 4#(x1) 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 0#(1(x1)) 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(0(1(x1))) 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(1(0(1(x1)))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(4(1(2(x1))))) -> 1#(x1) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 0#(4(x1)) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 3#(0(4(x1))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(5(2(2(4(1(0(x1))))))) -> 4#(x1) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(0(0(1(1(x1)))))) -> 3#(3(x1)) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(0(0(1(1(x1)))))) -> 3#(x1) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(0(3(0(0(2(x1))))))) -> 3#(x1) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(4(0(1(5(4(x1))))))) -> 1#(5(3(4(x1)))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(4(0(1(5(4(x1))))))) -> 3#(4(x1)) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(4(0(1(5(4(x1))))))) -> 5#(3(4(x1))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 0#(2(2(5(0(4(3(x1))))))) -> 5#(3(x1)) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(2(1(1(4(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(5(0(1(5(2(x1))))))) -> 0#(2(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(0(3(0(x1))))) -> 4#(3(0(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(4(x1))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(4(x1)) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(0(3(1(0(0(0(x1))))))) -> 4#(x1) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 1#(2(4(5(4(3(5(x1))))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(3(5(x1))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 4#(5(4(3(5(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(3(0(0(3(3(5(x1))))))) -> 5#(4(3(5(x1)))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(0(3(0(4(x1)))))) -> 1#(4(4(x1))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(0(3(0(4(x1)))))) -> 4#(4(x1)) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(1(3(0(4(3(x1))))))) -> 1#(x1) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(1(3(0(4(3(x1))))))) -> 5#(1(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 1#(0(x1)) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 1#(2(4(3(3(5(3(1(0(x1))))))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(1(0(x1))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(3(5(3(1(0(x1)))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 3#(5(3(1(0(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 4#(3(3(5(3(1(0(x1))))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(4(4(0(0(0(0(x1))))))) -> 5#(3(1(0(x1)))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(5(0(0(5(3(3(x1))))))) -> 1#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 0#(3(x1)) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 1#(0(3(x1))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(5(1(0(3(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 3#(x1) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 1#(2(4(4(0(5(1(x1))))))) -> 5#(1(0(3(x1)))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [1#](X) = X [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 1#(3(4(4(1(0(1(x1))))))) 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 1#(5(x1)) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 1#(0(3(1(1(2(x1)))))) 3#(1(4(0(1(2(x1)))))) -> 1#(1(2(x1))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(0(4(1(4(x1))))))) -> 1#(0(0(x1))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(1(2(1(0(0(x1)))))) 4#(0(0(0(4(1(4(x1))))))) -> 1#(2(1(0(0(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 1#(2(0(5(4(4(1(x1))))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 1#(5(x1)) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 1#(0(3(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(1(4(x1))) 4#(0(4(1(4(0(0(x1))))))) -> 1#(4(x1)) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 1#(4(x1)) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 1#(1(3(4(x1)))) 5#(0(2(5(4(4(0(x1))))))) -> 1#(3(4(x1))) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(0(0(3(1(x1))))) 5#(3(0(1(4(3(1(x1))))))) -> 1#(2(1(0(0(3(1(x1))))))) 5#(3(5(0(1(0(1(x1))))))) -> 1#(5(5(3(5(1(x1)))))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(0(0(1(3(5(x1)))))) -> 0#(5(3(1(5(x1))))) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(0(0(1(3(5(x1)))))) -> 3#(1(5(x1))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(0(0(1(3(5(x1)))))) -> 5#(3(1(5(x1)))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(1(4(0(1(2(x1)))))) -> 0#(3(1(1(2(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [3#](X) = X [4#](X) = X + 1 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 3#(4(4(1(0(1(x1)))))) 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(3(5(4(1(5(x1)))))) 4#(0(0(4(0(0(2(x1))))))) -> 3#(5(4(1(5(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 3#(4(4(0(x1)))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 3#(1(0(3(x1)))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(4(3(1(0(3(x1)))))) 4#(0(3(0(2(5(1(x1))))))) -> 3#(x1) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 3#(4(x1)) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 3#(3(4(x1))) 4#(3(5(5(4(1(0(x1))))))) -> 3#(4(x1)) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 4#(5(0(2(4(1(x1)))))) -> 3#(4(1(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 3#(0(5(4(x1)))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 3#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 3#(5(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pair Processor: -> Pairs: 3#(1(4(0(1(2(x1)))))) -> 3#(1(1(2(x1)))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X [3](X) = 2.X [4](X) = 2.X [5](X) = 0 [2](X) = 0 [3#](X) = 2.X Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(0(x1)) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [4#](X) = X + 1 [5#](X) = X + 1 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(0(4(1(4(x1))))))) -> 0#(x1) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(1(x1)) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 4#(4(1(x1))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 5#(4(4(1(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [4#](X) = X + 1 [5#](X) = X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 4#(1(5(x1))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(4(1(5(x1)))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(0(0(2(x1))))))) -> 5#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [4#](X) = X + 1 [5#](X) = X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(5(2(4(x1))))))) -> 0#(x1) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(0(x1)) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(0(4(5(2(4(x1))))))) -> 4#(4(0(x1))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 1 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(3(0(2(5(1(x1))))))) -> 0#(3(x1)) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 2.X [3](X) = 1 [4](X) = 2 [5](X) = 2 [2](X) = 1 [0#](X) = X [4#](X) = 2 [5#](X) = 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(3(0(2(5(1(x1))))))) -> 4#(3(1(0(3(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 0#(0(2(1(1(4(x1)))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 1 [1](X) = 2.X [3](X) = 0 [4](X) = 2 [5](X) = 2 [2](X) = 0 [0#](X) = X [4#](X) = 2 [5#](X) = 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(0(4(1(4(0(0(x1))))))) -> 4#(x1) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 2 [4#](X) = X + 1 [5#](X) = X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(0(5(4(1(4(x1))))))) -> 4#(3(4(x1))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(4(0(3(1(0(x1))))))) -> 4#(x1) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(4(0(3(1(0(x1))))))) -> 5#(1(4(x1))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 0 [3](X) = X [4](X) = 2 [5](X) = 2.X + 2 [2](X) = 0 [0#](X) = 2 [4#](X) = 2 [5#](X) = 2.X + 1 Problem 1.2: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 0#(5(4(x1))) 5#(0(0(0(1(4(0(x1))))))) -> 4#(x1) 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(0(2(5(4(4(0(x1))))))) -> 4#(x1) 5#(3(0(1(4(3(1(x1))))))) -> 0#(0(3(1(x1)))) 5#(3(0(1(4(3(1(x1))))))) -> 0#(3(1(x1))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) 5#(4(0(4(1(0(3(x1))))))) -> 4#(3(x1)) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->->Cycle: ->->-> Pairs: 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) The problem is decomposed in 2 subproblems. Problem 1.2.1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(2(5(4(0(0(x1))))))) -> 0#(4(x1)) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X Problem 1.2.1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2.1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(1(2(5(4(0(0(x1))))))) -> 4#(x1) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = X + 1 [4#](X) = X Problem 1.2.1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2.1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) 4#(3(5(5(4(1(0(x1))))))) -> 4#(x1) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [0#](X) = 2.X + 2 [4#](X) = 2.X Problem 1.2.1: SCC Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2.1: Reduction Pair Processor: -> Pairs: 0#(5(3(1(4(3(1(x1))))))) -> 4#(4(1(0(1(x1))))) 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X [1](X) = 2.X + 2 [3](X) = 2 [4](X) = 2 [5](X) = 2 [2](X) = 2 [0#](X) = 2.X + 2 [4#](X) = 2.X + 1 Problem 1.2.1: SCC Processor: -> Pairs: 4#(0(0(1(3(1(x1)))))) -> 0#(5(4(4(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2.2: Reduction Pair Processor: -> Pairs: 5#(0(0(0(1(4(0(x1))))))) -> 5#(4(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [5#](X) = 2.X Problem 1.2.2: SCC Processor: -> Pairs: 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2.2: Reduction Pair Processor: -> Pairs: 5#(3(5(0(1(0(1(x1))))))) -> 5#(1(x1)) 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 0 [3](X) = X [4](X) = 2 [5](X) = 2 [2](X) = 0 [5#](X) = 2.X Problem 1.2.2: SCC Processor: -> Pairs: 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2.2: Reduction Pair Processor: -> Pairs: 5#(3(5(0(1(0(1(x1))))))) -> 5#(3(5(1(x1)))) 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 0 [3](X) = 2.X [4](X) = X [5](X) = 2.X [2](X) = 0 [5#](X) = 2.X Problem 1.2.2: SCC Processor: -> Pairs: 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) ->->-> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) Problem 1.2.2: Reduction Pair Processor: -> Pairs: 5#(3(5(0(1(0(1(x1))))))) -> 5#(5(3(5(1(x1))))) -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) -> Usable rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [3](X) = X [4](X) = X + 1 [5](X) = X + 1 [2](X) = X [5#](X) = 2.X Problem 1.2.2: SCC Processor: -> Pairs: Empty -> Rules: 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(1(0(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite.