YES Problem 1: (VAR v_NonEmpty:S x1:S) (RULES 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ) Problem 1: Dependency Pairs Processor: -> Pairs: 0#(0(1(2(x1:S)))) -> 0#(x1:S) 0#(0(1(2(x1:S)))) -> 2#(3(0(x1:S))) 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: SCC Processor: -> Pairs: 0#(0(1(2(x1:S)))) -> 0#(x1:S) 0#(0(1(2(x1:S)))) -> 2#(3(0(x1:S))) 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(1(2(x1:S)))) -> 0#(x1:S) 0#(0(1(2(x1:S)))) -> 2#(3(0(x1:S))) 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(1(2(x1:S)))) -> 0#(x1:S) 0#(0(1(2(x1:S)))) -> 2#(3(0(x1:S))) 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(1(2(x1:S)))) -> 2#(3(0(x1:S))) 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(1(2(x1:S)))) -> 2#(3(0(x1:S))) 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(1(2(x1:S)))) -> 2#(3(0(x1:S))) 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = 2.X + 1 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(0(1(2(x1:S)))) -> 3#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(0(2(0(x1:S))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X [4#](X) = 2.X + 1 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(0(2(0(x1:S)))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(2(0(x1:S))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 1 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 0#(4(0(0(0(2(0(x1:S))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 1 [2#](X) = 2.X + 1 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 1#(2(3(0(4(0(0(0(2(0(x1:S)))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(0(x1:S)) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X [4#](X) = 2.X + 1 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 2#(3(0(4(0(0(0(2(0(x1:S))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 1 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(0(4(0(0(0(2(0(x1:S)))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(1(2(3(0(4(0(0(0(2(0(x1:S))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = 2.X + 1 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3#(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [0#](X) = 2.X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 0#(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 4#(0(0(0(2(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [0#](X) = X [1#](X) = X [2#](X) = 2.X + 2 [3#](X) = X + 2 [4#](X) = X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 0#(x1:S) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(1(2(3(4(3(1(x1:S))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 0#(3(0(1(2(3(4(3(1(x1:S))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(5(1(3(3(0(x1:S)))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 0#(x1:S) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(1(2(x1:S))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 0#(3(4(0(1(2(x1:S)))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 0#(3(x1:S)) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(4(2(3(4(3(4(2(0(x1:S))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 0#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 0#(x1:S) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 0#(x1:S) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(0(4(5(4(0(0(x1:S)))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(4(5(4(0(0(x1:S))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(4(5(4(0(0(x1:S)))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 0#(x1:S) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(1(4(0(3(x1:S))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 0#(3(x1:S)) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 0#(0(2(3(x1:S)))) 5#(2(2(1(2(x1:S))))) -> 0#(2(3(x1:S))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(3(3(5(0(4(1(x1:S))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(4(1(x1:S))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 0#(5(4(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 0#(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(1(0(0(2(1(1(0(3(2(2(1(3(x1:S))))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(2(1(1(0(3(2(2(1(3(x1:S)))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 0#(3(2(2(1(3(x1:S)))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 0#(4(1(4(5(4(x1:S)))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(3(4(4(0(x1:S)))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = 2.X + 1 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(3(4(4(0(x1:S))))) 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = 2.X + 1 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 3#(4(4(0(x1:S)))) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [1#](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(0(x1:S)) 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 1 [1](X) = 0 [2](X) = 2.X [3](X) = 0 [4](X) = 0 [5](X) = 2 [1#](X) = 2 [2#](X) = 2 [3#](X) = 2 [4#](X) = X [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 1#(3(5(4(1(2(2(x1:S))))))) -> 4#(4(0(x1:S))) 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 1 [2](X) = 2 [3](X) = 1 [4](X) = 1 [5](X) = 2 [1#](X) = 2 [2#](X) = 2 [3#](X) = 2 [4#](X) = X [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 1#(3(5(5(2(x1:S))))) -> 1#(3(2(3(x1:S)))) 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [1#](X) = X + 2 [2#](X) = X + 2 [3#](X) = X + 2 [4#](X) = X + 2 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 1#(3(5(5(2(x1:S))))) -> 2#(3(x1:S)) 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [1#](X) = 2.X [2#](X) = 2.X + 1 [3#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 1#(3(5(5(2(x1:S))))) -> 3#(2(3(x1:S))) 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [1#](X) = 2.X + 1 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 1#(3(5(5(2(x1:S))))) -> 3#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [1#](X) = 2.X + 1 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(2(3(4(3(1(x1:S)))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 1#(x1:S) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(3(3(0(x1:S)))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 1#(4(3(0(5(1(3(3(0(x1:S))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 1#(2(x1:S)) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(0(3(x1:S))) 2#(2(5(3(2(2(x1:S)))))) -> 1#(1(0(3(x1:S)))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 1#(2(4(1(x1:S)))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 1#(3(3(3(x1:S)))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 1#(3(3(4(x1:S)))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 1#(4(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 1#(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 1#(x1:S) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 1#(4(0(3(x1:S)))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 1#(0(3(3(5(0(4(1(x1:S)))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(3(0(4(x1:S)))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 1#(5(1(3(0(4(x1:S)))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 1#(4(3(3(1(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(0(3(2(2(1(3(x1:S))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(1(0(3(2(2(1(3(x1:S)))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 1#(3(x1:S)) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1#(5(5(0(4(1(4(5(4(x1:S))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(0(3(0(1(2(3(4(3(1(x1:S)))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X + 1 [3#](X) = 2.X + 1 [4#](X) = 2.X + 1 [5#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(3(4(3(1(x1:S))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = X + 2 [4#](X) = X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 2#(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X [3#](X) = 2.X [4#](X) = X + 1 [5#](X) = 2.X Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(0(1(2(3(4(3(1(x1:S)))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(3(1(x1:S))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 1 [1](X) = 0 [2](X) = 1 [3](X) = 0 [4](X) = 0 [5](X) = 1 [2#](X) = 2 [3#](X) = 2 [4#](X) = X + 1 [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 1 [1](X) = 0 [2](X) = 2.X [3](X) = 0 [4](X) = 0 [5](X) = 2 [2#](X) = 2 [3#](X) = 2 [4#](X) = X [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 4#(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S))))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = 2.X + 2 [5#](X) = 2.X Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(1(x1:S)) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [2#](X) = 2.X + 1 [3#](X) = 2.X + 1 [4#](X) = 2.X + 2 [5#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 3#(4(3(1(x1:S)))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = X + 2 [4#](X) = X + 2 [5#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))) 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 1 [1](X) = 0 [2](X) = 1 [3](X) = 0 [4](X) = 1 [5](X) = 1 [2#](X) = 2 [3#](X) = 2 [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5#(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = X + 2 [3#](X) = 2.X [4#](X) = X + 2 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(1(4(3(0(5(1(3(3(0(x1:S)))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = X + 2 [3#](X) = 2.X + 2 [4#](X) = X + 2 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2#(4(2(1(4(3(0(5(1(3(3(0(x1:S)))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(5(1(3(3(0(x1:S))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = X + 2 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(0(x1:S)) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X [3#](X) = X [4#](X) = X + 2 [5#](X) = X Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 3#(3(0(x1:S))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 1 [1](X) = 0 [2](X) = 2.X [3](X) = 0 [4](X) = 0 [5](X) = 2 [2#](X) = 2 [3#](X) = 2 [4#](X) = X [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 4#(3(0(5(1(3(3(0(x1:S)))))))) 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 1 [1](X) = 0 [2](X) = 2.X [3](X) = 0 [4](X) = 0 [5](X) = 2 [2#](X) = 2 [3#](X) = 2 [4#](X) = X [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 2#(x1:S) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 5#(1(3(3(0(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [2#](X) = X + 2 [3#](X) = X + 2 [4#](X) = 2.X [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 3#(4(0(1(2(x1:S))))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(1(2(x1:S)))) 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = X + 2 [5#](X) = 2.X Problem 1: SCC Processor: -> Pairs: 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(1(5(2(1(3(4(4(x1:S)))))))) -> 4#(0(3(4(0(1(2(x1:S))))))) 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = X + 1 [3](X) = X [4](X) = X [5](X) = X + 1 [2#](X) = X + 1 [3#](X) = X + 2 [4#](X) = X + 1 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(3(4(3(4(2(0(x1:S)))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 1 [1](X) = 0 [2](X) = 2.X [3](X) = 0 [4](X) = 0 [5](X) = 2 [2#](X) = 2 [3#](X) = 2 [4#](X) = X [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(2(5(3(2(2(x1:S)))))) -> 5#(1(1(0(3(x1:S))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 0 [2](X) = 2 [3](X) = 0 [4](X) = 2 [5](X) = 2 [2#](X) = 2 [3#](X) = 2 [4#](X) = 2 [5#](X) = X Problem 1: SCC Processor: -> Pairs: 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(2(5(3(2(2(x1:S)))))) -> 3#(x1:S) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = 2.X + 1 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(0(x1:S)) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 1 [1](X) = X + 1 [2](X) = X + 2 [3](X) = X + 1 [4](X) = X + 1 [5](X) = X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 2#(3(4(3(4(2(0(x1:S))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 1 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(0(4(2(3(4(3(4(2(0(x1:S)))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 1 [5#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(2(0(x1:S)))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 3#(4(3(4(2(0(x1:S)))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(2(0(x1:S))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 1 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 1 [1](X) = 0 [2](X) = 2.X [3](X) = 0 [4](X) = 0 [5](X) = 1 [2#](X) = 2 [3#](X) = 2 [4#](X) = X + 1 [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4#(3(4(2(0(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 2#(1(2(4(1(x1:S))))) 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 1 [2](X) = 2 [3](X) = 1 [4](X) = 2 [5](X) = 2 [2#](X) = X [3#](X) = 2 [4#](X) = 2 [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 2#(4(1(x1:S))) 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 4#(1(x1:S)) 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [2#](X) = 2.X + 2 [3#](X) = X + 1 [4#](X) = 2.X + 2 [5#](X) = X + 1 Problem 1: SCC Processor: -> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 2#(5(1(2(1(1(x1:S)))))) -> 5#(2(1(2(4(1(x1:S)))))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 0 [2](X) = 2.X [3](X) = 0 [4](X) = 0 [5](X) = 2 [2#](X) = 2.X + 2 [3#](X) = 2 [4#](X) = 2 [5#](X) = 2 Problem 1: SCC Processor: -> Pairs: 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 2#(4(3(0(x1:S)))) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 2#(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 2#(4(x1:S)) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 2#(4(5(1(x1:S)))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 2#(3(x1:S)) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 2#(1(0(3(3(5(0(4(1(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(1(0(3(2(2(1(3(x1:S))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(1(3(x1:S))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 2#(2(1(3(x1:S)))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(1(4(2(4(x1:S)))))) -> 3#(x1:S) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [3#](X) = X + 1 [4#](X) = X [5#](X) = X Problem 1: SCC Processor: -> Pairs: 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(3(x1:S))) 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [3#](X) = X + 2 [4#](X) = 2.X + 2 [5#](X) = X + 2 Problem 1: SCC Processor: -> Pairs: 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(4(1(4(2(4(x1:S)))))) -> 3#(3(x1:S)) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [3#](X) = 2.X [4#](X) = 2.X [5#](X) = 2.X Problem 1: SCC Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(1(3(3(4(x1:S))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [3#](X) = 2.X [4#](X) = 2.X + 1 [5#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(1(3(3(4(x1:S)))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [3#](X) = X [4#](X) = X + 2 [5#](X) = X Problem 1: SCC Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(3(1(3(3(4(x1:S))))))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(3(4(x1:S))) 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X Problem 1: SCC Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3#(4(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [3#](X) = 2.X [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(5(2(2(4(5(x1:S)))))) -> 3#(0(x1:S)) 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [3#](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1: SCC Processor: -> Pairs: 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1: Reduction Pair Processor: -> Pairs: 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 3#(5(2(2(4(5(x1:S)))))) -> 4#(3(0(x1:S))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 0 [2](X) = 2 [3](X) = 0 [4](X) = 2 [5](X) = 2 [3#](X) = 2 [4#](X) = 2.X + 1 [5#](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 3#(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(3(5(4(1(x1:S))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 3#(5(4(1(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(4(5(0(1(4(0(3(x1:S)))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 3#(x1:S) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(1(2(x1:S))))) -> 3#(x1:S) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(2(1(0(3(3(5(0(4(1(x1:S)))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(3(5(0(4(1(x1:S)))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 3#(5(0(4(1(x1:S))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(0(4(x1:S))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 3#(1(5(1(3(0(4(x1:S))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(3(1(x1:S))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(4(4(4(5(1(4(3(3(1(x1:S)))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3#(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(2(2(1(3(x1:S))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 3#(x1:S) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->->Cycle: ->->-> Pairs: 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pair Processor: -> Pairs: 3#(5(2(2(4(5(x1:S)))))) -> 3#(2(4(3(0(x1:S))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = X [2](X) = 2.X + 1 [3](X) = 0 [4](X) = 0 [5](X) = 2 [3#](X) = X Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(2(5(2(x1:S)))) -> 4#(0(x1:S)) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 0 [2](X) = 2.X [3](X) = 0 [4](X) = 0 [5](X) = 2 [4#](X) = X [5#](X) = 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(0(0(x1:S))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [4#](X) = X + 1 [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(0(0(0(4(5(4(0(0(x1:S)))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 1 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 1 [5](X) = X + 1 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4#(5(4(0(0(x1:S))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(0(0(0(4(5(4(0(0(x1:S))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S)))))))))))))) 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = X + 2 [3](X) = X [4](X) = X [5](X) = X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 5#(4(0(0(x1:S)))) 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(3(4(x1:S)))) -> 4#(4(2(4(x1:S)))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 1 [2](X) = 2 [3](X) = 1 [4](X) = 1 [5](X) = 2 [4#](X) = X [5#](X) = 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(3(4(x1:S)))) -> 4#(2(4(x1:S))) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(1(x1:S)) 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [4#](X) = 2.X [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(4(3(0(5(1(x1:S))))))) -> 4#(3(3(5(4(1(x1:S)))))) 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 0 [2](X) = 2.X [3](X) = 0 [4](X) = 0 [5](X) = 2 [4#](X) = X [5#](X) = 2 Problem 1.2: SCC Processor: -> Pairs: 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 4#(5(4(3(0(5(1(x1:S))))))) -> 5#(4(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [4#](X) = 2.X + 2 [5#](X) = 2.X + 2 Problem 1.2: SCC Processor: -> Pairs: 5#(2(1(0(1(5(x1:S)))))) -> 4#(2(4(5(1(x1:S))))) 5#(2(1(0(1(5(x1:S)))))) -> 4#(5(1(x1:S))) 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(0(3(x1:S))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 4#(5(0(1(4(0(3(x1:S))))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(1(x1:S)) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 4#(3(2(1(0(3(3(5(0(4(1(x1:S))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(3(3(1(x1:S)))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(4(5(1(4(3(3(1(x1:S))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(4(5(1(4(3(3(1(x1:S)))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 4#(5(1(4(3(3(1(x1:S))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 4#(1(4(5(4(x1:S))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(2(1(0(1(5(x1:S)))))) -> 5#(1(x1:S)) 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [5#](X) = X Problem 1.2: SCC Processor: -> Pairs: 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(2(1(0(1(5(x1:S)))))) -> 5#(4(2(4(5(1(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = 2.X + 2 [3](X) = 0 [4](X) = 2 [5](X) = 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(0(1(4(0(3(x1:S)))))) 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X [2](X) = 2.X + 2 [3](X) = X [4](X) = X [5](X) = 2.X + 2 [5#](X) = X Problem 1.2: SCC Processor: -> Pairs: 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5#(3(4(5(0(1(4(0(3(x1:S))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = 1 [2](X) = 2 [3](X) = 1 [4](X) = 2 [5](X) = 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(4(1(x1:S)))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = X + 2 [3](X) = X [4](X) = X [5](X) = X + 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = X + 2 [3](X) = X [4](X) = X [5](X) = X + 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5#(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))) 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(4(0(2(2(4(0(4(x1:S)))))))) -> 5#(1(3(0(4(x1:S))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2 [1](X) = X [2](X) = 2 [3](X) = 1 [4](X) = X [5](X) = 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 2 [1](X) = X + 2 [2](X) = X + 2 [3](X) = X + 2 [4](X) = X + 2 [5](X) = X + 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(1(4(3(3(1(x1:S)))))) 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = 2.X + 2 [1](X) = 2.X + 2 [2](X) = 2.X + 2 [3](X) = 2.X + 2 [4](X) = 2.X + 2 [5](X) = 2.X + 2 [5#](X) = X Problem 1.2: SCC Processor: -> Pairs: 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 5#(3(4(4(4(5(1(4(3(3(1(x1:S))))))))))) 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = 2.X + 2 [3](X) = 0 [4](X) = 2 [5](X) = 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5#(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = 2.X + 1 [3](X) = 0 [4](X) = 2 [5](X) = 1 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(0(4(1(4(5(4(x1:S))))))) 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X + 1 [1](X) = X [2](X) = X + 2 [3](X) = X [4](X) = X [5](X) = X + 2 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) ->->-> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) Problem 1.2: Reduction Pair Processor: -> Pairs: 5#(4(4(5(0(1(4(5(4(x1:S))))))))) -> 5#(5(0(4(1(4(5(4(x1:S)))))))) -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) -> Usable rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0](X) = X [1](X) = X [2](X) = 2.X + 1 [3](X) = 0 [4](X) = 2 [5](X) = 1 [5#](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: 0(0(1(2(x1:S)))) -> 2(3(0(x1:S))) 0(2(3(5(4(2(2(1(0(3(3(5(0(x1:S))))))))))))) -> 3(3(1(2(3(0(4(0(0(0(2(0(x1:S)))))))))))) 1(3(5(4(1(2(2(x1:S))))))) -> 3(3(3(4(4(0(x1:S)))))) 1(3(5(5(2(x1:S))))) -> 1(3(2(3(x1:S)))) 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1:S)))))))))))))))))))) -> 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1:S)))))))))))))))))))) 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1:S)))))))))))))) -> 2(2(4(2(1(4(3(0(5(1(3(3(0(x1:S))))))))))))) 2(1(5(2(1(3(4(4(x1:S)))))))) -> 4(0(3(4(0(1(2(x1:S))))))) 2(2(5(3(2(2(x1:S)))))) -> 5(1(1(0(3(x1:S))))) 2(4(1(2(5(2(4(1(3(2(0(3(x1:S)))))))))))) -> 4(3(0(4(2(3(4(3(4(2(0(x1:S))))))))))) 2(5(1(2(1(1(x1:S)))))) -> 5(2(1(2(4(1(x1:S)))))) 3(4(1(4(2(4(x1:S)))))) -> 1(3(3(3(x1:S)))) 3(4(2(1(1(2(2(5(4(x1:S))))))))) -> 3(3(3(1(3(3(4(x1:S))))))) 3(5(2(2(4(5(x1:S)))))) -> 3(2(4(3(0(x1:S))))) 4(2(5(2(x1:S)))) -> 1(4(0(x1:S))) 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1:S))))))))))))))) -> 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1:S))))))))))))))) 4(5(3(4(x1:S)))) -> 4(4(2(4(x1:S)))) 4(5(4(3(0(5(1(x1:S))))))) -> 4(3(3(5(4(1(x1:S)))))) 5(2(1(0(1(5(x1:S)))))) -> 5(4(2(4(5(1(x1:S)))))) 5(2(1(3(1(5(2(5(4(4(x1:S)))))))))) -> 5(3(4(5(0(1(4(0(3(x1:S))))))))) 5(2(2(1(2(x1:S))))) -> 0(0(2(3(x1:S)))) 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1:S))))))))))))))) -> 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1:S)))))))))))))) 5(4(0(2(2(4(0(4(x1:S)))))))) -> 3(1(5(1(3(0(4(x1:S))))))) 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1:S))))))))))))))))))) -> 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1:S)))))))))))))))))) 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1:S))))))))))))))) -> 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1:S)))))))))))))) 5(4(4(5(0(1(4(5(4(x1:S))))))))) -> 1(5(5(0(4(1(4(5(4(x1:S))))))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite.